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Proof step 30 from proof int2bytes-len-le (previous step)

(n→i(n) - 1) * 8 + 1 < 8 * (1 + n→i(# int2bytes(i) - 1)), 8 * n→i(# int2bytes(i) - 1) + 1 < 8 * (1 + n→i(# int2bytes(i) - 1)), 2 ^ ((n→i(n) - 1) * 8) ≤ i, # int2bytes(i) < n, 2 ^ (8 * n→i(# int2bytes(i) - 1)) ≤ i, 0 ≤ i, i < 2 ^ (8 * (1 + n→i(# int2bytes(i) - 1)) - 1) ⊦ int2bytes(i).first = i2b(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ n ≤ m → n→i(m - n) = n→i(m) - n→i(n) subst: [n, m] → [1, # int2bytes(i)] rotate: F spec: intnat inst: name: n2i-sub

Additional information

Used simplifier rules: int2bytes-empty: ⊦ int2bytes(i) ≠ [];% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i * j = j * i;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ m < 1 ↔ m = 0;% ⊦ # bytes = 0 ↔ bytes = []; Used terms: 1, # int2bytes(i)